The Parity of Invariant Characteristics
Abstract
We demonstrate a method to prove that a theta characteristic on Riemann surface S invariant under the action of G ≤ Aut(S) has even parity by considering the representation theory of the double cover G = 2 · G. We apply this to certain Hurwitz curves, and prove a recent conjecture of Broughton \& Disney-Hogg.
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